Theoretical Analysis On A Diffusive SIR Epidemic Model With Nonlinear Incidence In A Heterogeneous Environment

In this thesis,we are concerned with a diffusive SIR epidemic model with nonlin-ear incidence of the form I~pS~qfor 0<p?1 in a heterogeneous environment.We es-tablish the boundedness and uniform persistence of solutions to the system,and then the uniform persistence property in the two case:(i)0<p<1and(ii)p=1,and the global stability of the constant endemic equilibrium in the case of homogeneous environment.When the spatial environment is heterogeneous,we determine the asymptotic profile of endemic equilibrium if the diffusion rate of the susceptible or infected population is small.Our theoretical analysis shows that,different from the studies of[1,28,38,44]for the SIS models,restricting the movement of the susceptible or infected population can not lead to the extinction of infectious disease for such an SIR system.